IT 



will give a .«trady point (<n' rather line) with respect to that component of the 

 acttial hiirizontal motion which causes hodily translation of the other. 



We cannot, however, apply the same »levice, without an itniiortaut adilition 

 which will lie (lescrilied in a later rhajiter, to the ni('u>urenicnt nf vertical motions, 

 since for their rejristration the mass nuist lie left fri'c tu iiicivi' in llir dircitinn in 

 which gravity acts. 



§ 18. Friction Error. Increa.'ie of Eff'itlive Inertia hij the ii^c of a 

 ■■iecond mri'm pivotted on the fir.<t at the Steadi/ Line. 



In an aitiial iii^truuicnt the f'licti'iu at the joints by wliirli tlie mass is 

 I ivitted on the line IT, and also at the recording index, when our is used to 

 give a permanent trace of the disturliance, prevents the line // from remaining 

 strictly at rest. The friction at the joints will tend to make the ma.-^s acipiire 

 duiing displacement le.^s angular motion than is necessary to keep //at rest ; and 

 hence the practical instantaneous axis, wliirli docs remain uanuived, will lie lar- 

 ther awav than // from the axis of sujiport. ( "onsei|uently a measurement liased 

 on the assmnj tion that the line // is steady will c^rr liy lieing too small. l''rictioii 

 at the jjoint of the recording index will iiitniiliiio an error of the same kind. 

 If these errors weie imiform it '.Miuld lie easy to ascertain and allnw fur tliem, 

 hut they will in general varv in dilVerent miivemcnts and even in ditl'erent parts 

 of a single movement, since tliex- depend on the ratio of the forees due to fiietiou 

 to the resistance which tlie pivntted mass ullers to angular aeeeieratinn. Hence 

 tile friction error (with a given arrangement of joints and marking p<iinter) will 

 he great when a displacement occurs slowly, hut com]iaratively snmll in sudden 

 di~turl'anc<s, and practical ex[>erience has shown that in manv cases i'arthi|Uake 

 movements are so slow as to make the elimination of eonsideiaMe IVietion crrois 

 a matter of great difficulty. The effective inertia of the suspended mass nnist 

 l;e increa.se<l, and, rtdativi'ly to it, th<' friction reduced as far :ls |M)ssil)le. 



The most efl'ective position for the material of the pivotted mass is at the 

 instantaneous axis, and accor<lingIy we may improve the steadiness nf the line // 

 liv I ivotting there in neiUial i-ijuililii imn a second mass or jioh, fri'<' to turn alioiit 

 the lini- //, and therefnre e|uivalent to an ei|ual i|Uantity of matter concentrated 

 at that line itself. Moreover, the ma.ss of file oiiginal imdy |ii\dlt<'d al /'/' 

 (which is less advantageouslv distrilmledl mav liieu lie diiiiiiii--h( d a~ iniieh as we 

 iileasc, or rather as iiuich as i- consistent w itli riiriditv. 1 u doin<: tiiis, care nmst 

 of coiirM- he t;ikcn to preserve the kinetic relation iictwci'U the axes /'/' ami // 

 unchanged. -Vnrl if the mas- if the original jiivotted li. dy (ir frame, as we ma\ 

 now cull it, since its function is meii-iy to furnish an axis of support for the Ixili, 

 he very small com|)arcd with tin- mass of the hoi», a small error in the pusitiou 

 of // will not affect the stcadiius- ofthat line scnsihiy. With this dis|osition of 

 jmrts we xe«'iire the maximum of edict ivi- ineitia for a given t"ital mass and a 

 given dibtanee of the instantaneous axit> Iroin the axis of support. 



